House Republican leader John Boehner of Ohio, right, joined by House GOP Whip Eric Cantor (R) of Va., on Wednesday to talk about about the changes in the balance of power in Congress.

J. Scott Applewhite/AP

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Washington — Even with a broad and historic majority, House Republicans have formidable roadblocks to delivering on a top campaign promise: to repeal or dismantle comprehensive health-care reform.

An outright repeal would have to get past a Democrat-controlled Senate and, more formidably, the Democratic president, who made health-care reform his No. 1 domestic priority earlier this year. Republicans don’t have the two-thirds majority required in both Houses to override a presidential veto.

Yet outright repeal is likely to be the first floor vote – after the vote for speaker – when the new Congress convenes in January.

No legislation more symbolizes what Republicans – and especially the conservative tea party movement – have dubbed the overreach of an out-of-touch majority. It’s a key vote for an insurgent freshman class eager to demonstrate that the 2010 election is producing change Washington.

“The health-care bill that was enacted by the current Congress will kill jobs in America, ruin the best health-care system in the world, and bankrupt our country,” said Rep. John Boehner (R) of Ohio, the presumptive House speaker, at a press briefing with GOP leaders Wednesday morning. “That means that we have to do everything we can to try to repeal this bill and replace it with common-sense reforms that will bring down the cost of health insurance.”

Mr. Boehner, says former GOP majority leader Dick Armey, “will find that the House will repeal it with no less than 20 Democratic votes.” He adds, “Don’t worry about what the Senate does.”

Mr. Armey advised and backed many tea party candidates.

For his part, President Obama is standing firm on the health-care law. “I’m sure this is an issue that will come up in discussions with Republican leadership, but I think we’d be misreading the election if we thought that the American people want to see us for the next two years relitigate arguments that we had over the last two years,” he said at a press briefing Wednesday afternoon.

“If Republicans have ideas for how to improve our health-care system ... I’m happy to consider some of those ideas,” he added.

Still, a strong move by Republicans on health care may be essential to sweeten what could be a bitter vote for the new GOP class: raising the national debt limit, now set at $14.9 trillion. Although conservatives campaigned aggressively against a soaring national debt, Mr. Armey predicts that tea party freshmen will back a new debt limit.

“It’s a legacy vote of the irresponsible spending that came before this time. Just in terms of avoiding breakdown, this vote has got to be made,” he adds.

House Democrats may opt to move this item in a lame-duck session, before the new lawmakers arrive.

In their “governing agenda,” House Republican leaders have already committed to repealing the “job killing” health-care law. “Because the new health care law kills jobs, raises taxes, and increases the cost of health care, we will immediately take action to repeal this law,” Republicans promised in their “Pledge to America,” which they released in September.

But they are also proposing that Congress enact elements left out of the Obama health-care law, such as medical liability reforms, the option of purchasing health-care insurance across state lines, and the expansion of health savings accounts.

The 3,833 pages of federal regulations issued to carry out the health-care law are also in the cross hairs of the new Congress. To date, Republicans have focused attention on ending a requirement for businesses to issue tax forms for any purchases over $600.

“One of the things that’s come up is that the 1099 provision in the health-care bill appears to be too burdensome for small businesses,” Mr. Obama acknowledged Wednesday. “That’s something we should take a look at.”

For Republicans, there is wide scope for delaying or derailing implementation of health-care reform. Toward that end, GOP committee chairs are already gearing up to sharply increase the level of oversight on the Obama administration.

Representative Issa describes health-care reform as an “unparalleled encroachment of the federal government in the private sector and the lives of individual Americans,” to be met by “vigorous congressional oversight” –including use of his panel’s subpoena power.

“Chairmen like Darrell Issa and others can haul Kathleen Sebelius [secretary of Health and Human Services], hold lots of hearings, do oversight to the max,” says Ross Baker, a political scientist at Rutgers University in New Brunswick, N.J. “Call it death by a thousand cuts. Even without statutory changes, you can make it very difficult to get health-care reform implemented.”

Grover Norquist, president of Americans for Tax Reform, an antitax group, also sees potential in what House Republicans can do on the health-care front. “Even if you don’t have the votes to make the Senate enact things, you do have enough votes to kick up a fuss that something’s going on [in the health-care law] that Americans don’t know about,” he says.

Another pressure point for health-care reform is implementation at the state level. Twenty-one states are currently challenging the law in courts, most notably because of the law’s mandate that Americans obtain health insurance.

With Republicans on track to hold at least 28 governorships and 25 state legislatures, resistance at the state level could accelerate.

In a poll of Americans released Wednesday, 36 percent of GOP respondents said repeal of health-care reform should be the No. 1 priority of the new Congress. Twenty-nine percent of Republicans cited reductions in federal spending. Democrats, meanwhile, overwhelmingly favored passing a new stimulus bill to create jobs (63 percent). But 12 percent of Democrats also cited repeal of health-care reform as their top priority for lawmakers.

“These partisan differences highlight the challenges that face the lame-duck Congress that will reconvene before the end of the year, as well as the new Congress that will take office in January,” said Frank Newport, editor in chief of Gallup, in a statement with the release.